Coupled-Chain Constructions of Fracton Spin Liquids

Fracton spin liquids are topologically ordered phases in three dimensions that go beyond the standard paradigm of topological order; they feature unconventional fractional excitations that are either completely immobile or only mobile along lower-dimensional subsystems, such as lines or planes. While there are several exactly solvable models of such fracton spin liquids, including Haah's cubic code and the X-cube model, these models are far from realistic as they involve interactions between many spins at the same time. In our work, we present a general coupled-spin-chain construction for realizing a large class of fracton spin liquids in more realistic models involving only two-spin interactions. Furthermore, we demonstrate that these coupled-spin-chain constructions directly translate into generalized parton constructions and hence illuminate the physical properties of the corresponding fracton spin liquids.